Question: Solve for $x$ and $y$ using elimination. ${-4x+y = -17}$ ${5x-y = 22}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-4x+y = -17}\thinspace$ to find $y$ ${-4}{(5)}{ + y = -17}$ $-20+y = -17$ $-20{+20} + y = -17{+20}$ ${y = 3}$ You can also plug ${x = 5}$ into $\thinspace {5x-y = 22}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ - y = 22}$ ${y = 3}$